Does base extension preserve exactness of s.e.s?

61 Views Asked by At

Let $k$ be a field. Say we have a s.e.s. of $k$-group schemes of finite type $1 \to G' \to G \to G'' \to 1$. Let $K \to k$ be a base extension.

Is $1 \to G'_K \to G_K \to G''_K \to 1$ still exact? Here $G_K = G \times_k K$ etc.